Your Fritzing looks clear. The connections look fine to me.
Providing your constructor() is accurate, Marek's ILI9341_due.h, Bodmer's TFT_ILI9341.h, Adafruit's Adafruit_ILI9341.h, ... should all work.
In fact most of these libraries will make some form of diagnostic report on the Serial Terminal. (you need to connect MISO line to #12. you do not need the 4050)
David.